Question: Show that if 0 y Rn and z Rn, then z = z1 + z2, where z1 = (ytz/ ||y||22)y is parallel

Show that if 0 ≠ y ∈ Rn and z ∈ Rn, then z = z1 + z2, where z1 = (ytz/ ||y||22)y is parallel to y and z2 is orthogonal to y.

Step by Step Solution

★★★★★

3.31 Rating (169 Votes )

There are 3 Steps involved in it

1 Expert Approved Answer
Step: 1 Unlock

If z t y 0 then z z 1 z 2 ... View full answer

blur-text-image
Question Has Been Solved by an Expert!

Get step-by-step solutions from verified subject matter experts

Step: 2 Unlock
Step: 3 Unlock

Document Format (1 attachment)

Word file Icon

731-M-N-A-N-L-A (951).docx

120 KBs Word File

Students Have Also Explored These Related Numerical Analysis Questions!

Q:

Let H V Rn, with H convex and V open, and suppose that : V Rn is C1. a) Show that if E is a closed subset of H and then h(x)/||h|| 0 uniformly on E, as h 0. b) Show that if R is a closed...

Q:

Given a vector x Rn+l, the (n + l) Ã (n + l) matrix V defined by is called the Vandermonde matrix. (a) Show that if Vc = y and p(x) = c1 + c2x + ... + cn+1xn then p(xi) = yi, i = 1, 2, ..., n...

Q:

Define IP: Rn x Rn R by IP (x, y) = . (a) Find D(IP) (a,b) and (IP) (a,b). (b) If f,g: R Rn are differentiable, and h: R R is defined by h(t) = , show that hI (a) =

Q:

The Basics of Financial Mathematics Spring 2003 Richard F. Bass Department of Mathematics University of Connecticut c These notes are 2003 by Richard Bass. They may be used for personal use or class...

Q:

\fCOMPLEX VARIABLES AND APPLICATIONS Eighth Edition James Ward Brown Professor of Mathematics The University of Michigan-Dearborn Ruel V. Churchill Late Professor of Mathematics The University of...

Q:

\fCOMPLEX VARIABLES AND APPLICATIONS Eighth Edition James Ward Brown Professor of Mathematics The University of Michigan-Dearborn Ruel V. Churchill Late Professor of Mathematics The University of...

Q:

8 April 14, 2016 In this assignment, we will learn some techniques for calculating line integrals and as an application compute some real integrals with complex techniques. Simply connected domains....

Q:

MATH 135 S 2016: Assignment 9 Solutions 1. Prove that for any integer n, 441n43 + 374n35 + 285n23 0 (mod 55). Solution: Since 55 = 5 11 and gcd(5, 11) = 1, we may use the Splitting Modulus...

Q:

Consider the data found in Table B.15 detailing mortality and air pollution on a by city/demographic basis. Following Example 9.3, use principle-components regression in comparison with standard...

Q:

Q9some type is wrong, can refer to the attach file. In a study of the relationship between an explanatory variable Z and a response variable Y , n independent observations are taken in the form of...

Q:

Find the inverses of the matrices in Exercises Use the algorithm introduced in this section. 1 2 [43] 7 5 [$ 10 4 7

Q:

A metal bar is placed at a temperature of 150 C in an oven with a constant temperature of O C. If after 30 minutes the temperature of the bar is 100 C, determine: a) the time required for the bar to...

Q:

Current Attempt in Progress Journalize the following transactions for Lily, Ine. ( a ) Incurred direct labor costs of $ 2 3 , 6 5 0 for 4 , 3 0 0 hours. The standard labor cost was $ 2 4 , 9 6 0 ....

Q:

2. Why might the leader fi nd a market system inconceivable? Is it possible for economic activities not based on self-interest to take place in a market economy?

Q:

Prove Fermats Theorem for the case in which f has a local minimum at c.

Q:

A cubic function is a polynomial of degree 3; that is, it has the form f(x) = ax3 + bx2 + cx + d, where a 0. (a) Show that a cubic function can have two, one, or no critical number(s). Give examples...

Q:

Verify that the function satisfies the three hypotheses of Roles Theorem on the given interval. Then find all numbers that satisfy the conclusion of Roles Theorem. 1. f(x) = x? - 4x + 1, [0. 4] 2....

Q:

Cyber Security and Crime option One: In this web research project, identify at least four types of cybercrimes. Using at least two sources on the Internet, briefly research cybercrimes, and write a...

Q:

The table below shows market prices for four zero coupon bonds with four different terms: one, two three and four years. The bonds all have a face value of $1,000. Calculate the yields on the zero...

Q:

1. Read through the article, Interaction of Oxytocin Leven and Past Depression May Predict Postpartum Depressive Synnitoni Severity (Massey et a1, 2016), and answer the following questions. a. Name...